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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Set convergences. An attempt of classification


Authors: Yves Sonntag and Constantin Zălinescu
Journal: Trans. Amer. Math. Soc. 340 (1993), 199-226
MSC: Primary 54A20; Secondary 54B20, 54D55, 54E15
DOI: https://doi.org/10.1090/S0002-9947-1993-1173857-8
MathSciNet review: 1173857
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Abstract: We endow families of nonempty closed subsets of a metric space with uniformities defined by semimetrics. Such structure is completely determined by a class (which is a family of closed sets) and a type (which is a semimetric). Two types are sufficient to define (and classify) almost all convergences known till now. These two types offer the possibility of defining other set convergences.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1173857-8
Keywords: Convergences on hyperspace, classes of subsets, types of semimetrics, classification
Article copyright: © Copyright 1993 American Mathematical Society